This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A106464 #32 Sep 02 2024 00:20:03
%S A106464 1,1,2,3,3,4,6,6,5,11,6,9,15,12,8,18,9,21,22,15,11,32,20,18,27,31,14,
%T A106464 45,15,32,36,24,41,57,18,27,43,60,20,66,21,51,72,33,23,84,42,60,57,61,
%U A106464 26,81,67,88,64,42,29,135,30,45,105
%N A106464 Antidiagonal sums of number triangle A003989.
%C A106464 Consider the triangle T(n, k) = A003989(n, k) = gcd(n-k+1, k), n >= 1, k = 1..n. Then a(n) = Sum_{k=0..floor(n/2)} T(n-k+1, k+1), for n >= 0. - _R. J. Mathar_, May 11 2018 [adjusted to the definition of A003989. - _Wolfdieter Lang_, May 12 2018]
%H A106464 Robert Israel, <a href="/A106464/b106464.txt">Table of n, a(n) for n = 0..10000</a>
%F A106464 a(n) = Sum_{k=0..floor(n/2)} gcd(n-2*k+1, k+1). [corrected by _R. J. Mathar_, May 11 2018]
%p A106464 f:= n -> add(igcd(n-2*k+1,k+1),k=0..n/2):
%p A106464 map(f, [$0..100]); # _Robert Israel_, May 11 2018
%t A106464 Array[Sum[GCD[# - 2 k + 1, k + 1], {k, 0, Floor[#/2]}] &, 61, 0] (* _Michael De Vlieger_, May 14 2018 *)
%o A106464 (PARI) a(n) = sum(k=0, n\2, gcd(n-2*k+1, k+1)); \\ _Michel Marcus_, May 11 2018
%o A106464 (GAP) Flat(List([0..70],n->Sum([0..Int(n/2)],k->Gcd(n-2*k+1,k+1)))); # _Muniru A Asiru_, May 15 2018
%Y A106464 Cf. A003989, A106466.
%K A106464 easy,nonn
%O A106464 0,3
%A A106464 _Paul Barry_, May 03 2005
%E A106464 Name corrected by _R. J. Mathar_, May 11 2018